A pre-order relation for exact schedulability test of sporadic tasks on multiprocessor Global Fixed-Priority scheduling

International audienceIn this paper we present an exact schedulability test for sporadic real-time tasks scheduled by the Global Fixed Priority (G-FP) Fully Preemp-tive Scheduler on a multiprocessor system. The analysis consists in mod-eling the system as a Linear Hybrid Automaton (LHA), and in performing a reachability analysis for states representing deadline miss conditions. To mitigate the problem of state space explosion, we propose a pre-order relationship over the symbolic states of the model: states that are simulated by others can be safely eliminated from the state space. We also formulate the concept of decidability interval with respect to a set of constrained-deadline sporadic tasks on multiprocessor. The decidability interval is a bounded time interval such that, if a deadline miss occurs in the schedule, then it is possible to find a configuration of arrival times for the tasks such that the deadline miss happens within the bounded interval. Vice versa, if no configuration of arrival times produces a deadline miss in the bounded interval, then no deadline miss is ever possible in the schedule. Hence we prove that the schedulability analysis problem is decidable, and we provide a formula for computing the decidability interval. To our knowledge, this is the first time such a time interval is proposed for sporadic tasks running on multiprocessor. The proposed schedulability analysis has been implemented in a software tool. For the first time we assess the pessimism of the state-of-the-art approximate schedulability test through experiments. Moreover, we show * This paper has been accepted by the Real Time Systems Journal. This is the submitted version, the final accepted version is avaliable at the journal's web site

A pre-order relation for exact schedulability test of sporadic tasks on multiprocessor Global Fixed-Priority scheduling

International audienceIn this paper we present an exact schedulability test for sporadic real-time tasks scheduled by the Global Fixed Priority (G-FP) Fully Preemp-tive Scheduler on a multiprocessor system. The analysis consists in mod-eling the system as a Linear Hybrid Automaton (LHA), and in performing a reachability analysis for states representing deadline miss conditions. To mitigate the problem of state space explosion, we propose a pre-order relationship over the symbolic states of the model: states that are simulated by others can be safely eliminated from the state space. We also formulate the concept of decidability interval with respect to a set of constrained-deadline sporadic tasks on multiprocessor. The decidability interval is a bounded time interval such that, if a deadline miss occurs in the schedule, then it is possible to find a configuration of arrival times for the tasks such that the deadline miss happens within the bounded interval. Vice versa, if no configuration of arrival times produces a deadline miss in the bounded interval, then no deadline miss is ever possible in the schedule. Hence we prove that the schedulability analysis problem is decidable, and we provide a formula for computing the decidability interval. To our knowledge, this is the first time such a time interval is proposed for sporadic tasks running on multiprocessor. The proposed schedulability analysis has been implemented in a software tool. For the first time we assess the pessimism of the state-of-the-art approximate schedulability test through experiments. Moreover, we show * This paper has been accepted by the Real Time Systems Journal. This is the submitted version, the final accepted version is avaliable at the journal's web site